%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT140^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:56 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT140^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 18:01:54 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.31 % (3515649)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (3515660)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=713521812:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (3515655)% WARNING: option uhcvi not known.
% 0.20/0.31 % (3515659)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4026710065:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (3515654)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1116782646_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (3515656)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3238080536:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (3515657)dis+10_1_sil=32000:sp=arity:random_seed=453283647:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (3515655)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4053636067:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (3515658)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2822801675:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (3515660) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3515649-3515660"...
% 0.20/0.31 % (3515655)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (3515658)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (3515660)...printing done.
% 0.20/0.31 % (3515660)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.20/0.31 thf(type_def_6, type, nat: $tType).
% 0.20/0.31 thf(type_def_7, type, itself: $tType > $tType).
% 0.20/0.31 thf(type_def_8, type, a: $tType).
% 0.20/0.31 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_7, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_8, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_9, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_11, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_12, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.31 thf(func_def_13, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_14, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_15, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_16, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_17, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_18, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.20/0.31 thf(func_def_19, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_20, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_21, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_22, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_23, type, coindu63249387sorted: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.31 thf(func_def_24, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_25, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_26, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_28, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.20/0.31 thf(func_def_29, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.20/0.31 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.20/0.31 thf(func_def_34, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_37, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_38, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_39, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_40, type, vAND: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_42, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_43, type, vOR: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_44, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_45, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_46, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_47, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_48, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_49, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_50, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_51, type, sK4: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_52, type, sK5: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_53, type, sK6: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_54, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_55, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_56, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_57, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_58, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_59, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_60, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_61, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_62, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_63, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_64, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_65, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_66, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_67, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_68, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_69, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_70, type, sK23: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_71, type, sK24: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_72, type, sK25: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_73, type, sK26: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_74, type, sK27: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_75, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_76, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_77, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_78, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_79, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_80, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_81, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_82, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_83, type, sK36: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_84, type, sK37: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_85, type, sK38: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_86, type, sK39: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_87, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_88, type, sK41: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_89, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_90, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_91, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_92, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_93, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_94, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.20/0.31 thf(func_def_95, type, sK48: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_96, type, sK49: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_97, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_98, type, sK51: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_99, type, sK52: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.20/0.31 thf(func_def_100, type, sK53: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.20/0.31 thf(func_def_101, type, sK54: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_102, type, sK55: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_103, type, sK56: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_104, type, sK57: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_105, type, sK58: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_106, type, sK59: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_107, type, sK60: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_108, type, sK61: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_109, type, sK62: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_110, type, sK63: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_111, type, sK64: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_112, type, sK65: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_113, type, sK66: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_114, type, sK67: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_115, type, sK68: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_116, type, sK69: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_117, type, sK70: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_118, type, sK71: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_119, type, sK72: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_120, type, sK73: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_121, type, sK74: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_122, type, sK75: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_123, type, sK76: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_124, type, sK77: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_125, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_126, type, sK79: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.20/0.31 thf(func_def_127, type, sK80: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_128, type, sK81: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_129, type, sK82: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_130, type, sK83: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_131, type, sK84: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_132, type, sK85: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_133, type, sK86: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_134, type, sK87: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_135, type, sK88: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_136, type, sK89: !>[X0: $tType]:((X0 > X0))).
% 0.20/0.31 thf(func_def_137, type, sK90: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.20/0.31 thf(func_def_138, type, sK91: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_139, type, sK92: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_140, type, sK93: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_141, type, sK94: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.31 thf(func_def_142, type, sK95: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_143, type, sK96: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_144, type, sK97: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_145, type, sK98: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_146, type, sK99: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_147, type, sK100: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_148, type, sK101: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.31 thf(func_def_149, type, sK102: ((nat > nat) > nat)).
% 0.20/0.31 thf(func_def_150, type, sK103: ((nat > nat) > nat)).
% 0.20/0.31 thf(func_def_151, type, sK104: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_152, type, sK105: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_153, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 0.20/0.31 thf(func_def_154, type, sK107: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.20/0.31 thf(func_def_155, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 0.20/0.31 thf(func_def_156, type, sK109: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.20/0.31 thf(f1,axiom,(
% 0.20/0.31 ! [X0 : $tType] : (ord_less_eq @ coinductive_llist @ X0 = coinductive_lprefix @ X0)),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_less__eq__llist__def)).
% 0.20/0.31 thf(f274,conjecture,(
% 0.20/0.31 (ord_less_eq @ coinductive_llist @ a = coinductive_lprefix @ a)),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.31 thf(f275,negated_conjecture,(
% 0.20/0.31 ~ (ord_less_eq @ coinductive_llist @ a = coinductive_lprefix @ a)),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f274])).
% 0.20/0.31 thf(f819,plain,(
% 0.20/0.31 (ord_less_eq @ coinductive_llist @ a != coinductive_lprefix @ a)),
% 0.20/0.31 inference(flattening,[],[f275])).
% 0.20/0.31 thf(f1201,plain,(
% 0.20/0.31 ( ! [X0 : $tType] : ((ord_less_eq @ coinductive_llist @ X0 = coinductive_lprefix @ X0)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f1])).
% 0.20/0.31 thf(f1582,plain,(
% 0.20/0.31 (ord_less_eq @ coinductive_llist @ a != coinductive_lprefix @ a)),
% 0.20/0.31 inference(cnf_transformation,[],[f819])).
% 0.20/0.31 thf(f1659,plain,(
% 0.20/0.31 (ord_less_eq @ coinductive_llist @ a != ord_less_eq @ coinductive_llist @ a)),
% 0.20/0.31 inference(definition_unfolding,[],[f1582,f1201])).
% 0.20/0.31 thf(f1687,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1659])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (3515660)------------------------------
% 0.20/0.31 % (3515660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (3515660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (3515660)CaDiCaL version: 2.1.3
% 0.20/0.31 % (3515660)Termination reason: Refutation
% 0.20/0.31 % (3515660)Time elapsed: 0.021 s
% 0.20/0.31 % (3515660)Peak memory usage: 13 MB
% 0.20/0.31 % (3515660)Instructions burned: 90 (million)
% 0.20/0.31 % (3515649)Success in time 0.057 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------